Used Back Rub Machine for sale (85,629)

Condition: excellent (used), Year of construction: 2018, Operating hours: 19,000 h Godpfxjxvp Tpe Aayeca

Condition: like new (used), Year of construction: 2020, functionality: fully functional, Alfred Gruber GmbH: Used Bottle Filler ARFD 6 – High-Performance Filling Line for Breweries and Beverage Producers We offer you a fully automatic bottle filler ARFD 6 made from stainless steel (AISI 403) by the renowned Alfred Gruber GmbH. This robust, high-performance system is the ideal solution for breweries, cideries, soda and water producers, and other beverage manufacturers looking to automate and optimize their filling processes. The ARFD 6 is available immediately and can be delivered at short notice. Gcsdpexpx Enefx Aayoa Key Features and Advantages at a Glance • Fully Automatic Operation: The ARFD 6 fully automates rinsing, filling, and capping of your bottles and party kegs. This significantly reduces personnel requirements and increases your production efficiency. • Versatile Filling: For both carbonated and non-carbonated beverages, and all types of liquids. o Bottles: The machine is ideal for filling bottles ranging from 0.33 liters to 3.0 liters. Smaller bottles (0.33l – 1.0l) are processed fully automatically, while larger bottles (1.5l – 3.0l) are filled semi-automatically. o Party kegs: 5.0-liter party kegs can also be filled semi-automatically. • Impressive Capacity: o Bottles (0.33l): Up to 1,100 bottles per hour. o Bottles (0.5l): Up to 900 bottles per hour. o Party kegs (5.0l): Up to 160 party kegs per hour. This high throughput ensures efficient production even during peak demand. • Integrated Ring-Pull Capper: The ARFD 6 is equipped with a special capping module for ring-pull closures. This provides your customers with a practical and easy-to-open seal. • Hot Water Injection: An integrated hot water injection system before capping ensures added hygiene and optimal sterilization of the bottle neck, improving the shelf life of your products. • Hygienic Design and Filling Quality: o CO2 Double Pre-Rinsing: Bottles undergo double pre-rinsing with CO2 before actual filling. This minimizes oxygen uptake, which is crucial for the quality and shelf life of beer and other sensitive beverages. o Adjustable Vent Valve: A precisely adjustable vent valve allows optimal flow control and minimizes foam formation during the filling process. o CIP Capable (Clean-in-Place): The system is fully CIP capable, allowing easy and efficient internal cleaning and sterilization. This greatly reduces cleaning efforts. o Low Beer Loss: The system is engineered to minimize product losses at the start and during the filling process. o Modern Control System: An intuitive Siemens PLC control with color touch panel enables easy operation and monitoring of all process steps. o Robust Construction: The entire system is made from high-quality stainless steel (AISI 403), ensuring durability, corrosion resistance, and easy cleaning, fully meeting food industry hygiene standards. Ideal Applications The ARFD 6 is perfectly suited for filling beer, cider, sodas, juices, and other carbonated or still beverages.

Condition: new, Year of construction: 2013, 4.Measurements: 1. Pre-modification; the present flatness accuracy of the substrate supporting surface and the linearity of the rubbing roll to the supporting surface are measured to determine the actual status 1.1.1. Measurement performed with and without a (largest) substrate 1.1.2. Measurement performed under process / ambient conditions 2. Post modification; the modified flatness accuracy of the substrate supporting surface and the linearity of the rubbing roll to the supporting surface are measured to determine the improved status Gcodpfx Ajwam N Seayja 2.1.1. Measurement performed with and without a (largest) substrate 5. Ambient conditions: 1. Temperature: 20 ± 5oC 2. Humidity: 50 ± 25%RH 6.Acceptance: 1. Approval of design drawings by customer before supplier starts manufacturing 1.1. The design approval will not free the supplier of his obligations to fulfill all parts of the deliverable 2. Site Acceptance Test (SAT) 2.1.Complete modification delivered / installed / pre-tested 2.2.Delivery of documentation (technical drawings of modified parts) 2.3.Acceptance tests 2.3.1. Accuracy measurements post modification with and without the largest (glass) substrate 2.3.2. Demonstration functionality on substrate sizes; 2.3.2.1. 10pcs. 300x300x4.0mm 2.3.2.2. 10pcs. 800x800x4.0mm 2.3.2.3. 10pcs. 1,200 x 1,500 x 4.0mm 2.3.2.4. 10pcs. substrate variations such as 2.0mm and/or tempered

Condition: used, Year of construction: 1980, machine/vehicle number: 19780, grinding length:600 mm grinding width:300 mm workpiece height:375 mm number of spindle speeds:1000 - 3000 UpM grinding wheel dimensions::300 x 50 x 76,2 mm Gedpfxscxxrzs Aayeca grinding spindle drive:2,8 - 8,4 kW weight of the machine ca.:3,5 t CNC-controlled, 3D-controlled profile-dressing unit, Unicom ELB-CNC control with integrated 024 CNC Unicon electric hand wheel, display screen, analogue spindle load display, stepless adjustable cross feed, coolant device with magnetic-roller chip collector, full housing, separate electrical cabinet, additional grinding wheel with flange

Condition: excellent (used), Year of construction: 2023, functionality: fully functional, working width: 380 mm, area performance: 1,500 m²/h, overall weight: 80 kg, tank capacity: 16 l, Video on request Technical data: Working width (cm): 38 Suction width (cm): 47 Surface performance (m²/h): 1,500 Cobjv Rx Rqenr E Sk Torh Number of protective plates (pcs): 1 Fresh water tank capacity (l): 16 Dirty water tank capacity (l): 22 Weight without batteries (kg): 40 Machine ready for use weight (kg): 80 Power (kW): 0.54 Gedpfoxlu Nzjx Aayjca Description The Hako Scrubmaster B12 scrubber dryer is a highly efficient machine suitable even for the most demanding jobs in large-scale facilities. During the complete inspection and refurbishment, our service team thoroughly checked every function of the machine. All worn mechanical parts were replaced with new ones. This ensures long and trouble-free operation without requiring additional investment in the machine in the future. The unit is now in perfect condition and ready for immediate operation.

Condition: good (used), Year of construction: 1992, 1,0 St. gebr. Flachschleifmaschine Godpji Ra Tysfx Aaysca Hersteller: ELB Typ: SUPER - RUBIN 024 CNC Baujahr: 1992 Verfahrwege: Schleiflänge: 600 mm Schleifbreite: 275 mm Schleifhöhe: 375 mm Tischaufspannfläche: 900 x 300 mm Tischbelastung: 300 kg Vertikal - Vorschub: max. 300 mm/min. Quervorschub: max. 2.000 mm/min. Steuerung: UNICON Im Lieferumfang sind Schleifscheiben enthalten siehe Fotos.

Condition: excellent (used), Year of construction: 1998, I sell Polymac Rubber edgebander little used, like new. Gedouvdzuepfx Aayeca

Condition: new, Year of construction: 2025, Take advantage of our Try&Buy offer and test the TruBend 7050 from 149.900€* incl. TRUMPF tool package incl. 90 days right of return *Offer only valid for new customers in Germany. The images shown correspond to extended equipment options and not the standard scope of the offer. Please contact us for details of the offer and further information. Gcodei Ubhxepfx Aayja About the machine: With the TruBend Series 7000, you can bend small and medium-sized parts highly productively under the best working conditions. Winner of the Ergonomics Award, it takes the strain off your operator while working quickly and safely. You achieve energy savings of up to 74% compared to conventional hydraulic drives and achieve precise results for all applications. See the perfect interaction between man and machine for yourself! Precise and intuitive Control, tool clamping, positioning and angle measurement - every work step supports the path to the perfect result. User-friendly handling and precise design make the machine a compact high performer in your production. Consistently ergonomic If the bender is comfortable, the bending process runs smoothly: the TruBend Series 7000 was the first bending machine to receive an ergonomics certificate. The operator works comfortably with a standing and sitting aid and adjusts the support table individually. The sitting and standing aid as well as the swivel-mounted control protect the spine. LED lighting guarantees optimum visibility in the work area. Further information can be found on our website. TRUMPF quality Our fast remote service support takes care of your concerns anywhere in the world. For further technical data, please refer to the data sheet or visit our website. If you have any questions, please contact us. About TRUMPF: In our 100-year company history, we have been able to help shape many thousands of sheet metal fabrications in Germany alone. We pass this experience on to our customers every day. With innovative machines and functions, the most comprehensive service concept on the market and experts in software, automation and Smart Factory, you will always receive an individual offer that is tailored to your requirements and makes you fit for the future. PS: We are also happy to support you when it comes to financing. With the financing, leasing or pay-per-use models of TRUMPF Financial Services, we are at your side for both financial and business challenges.

Condition: ready for operation (used), Year of construction: 2006, Two inserting machines are available. 1) Grützmacher Rubin C5, max. mechanical output: 7500pieces/h, envelope format range: C6-C5, min. insert size: 99mm/148mm, max. insert size: 148mm/210mm, max. filling thickness: 5mm. 2) Bell and Howell CEXP-6RC, year of manufacture: 2006, max. mechanical output: approx. 10000cycles/h, envelope format range: C6-C5, max. insert dimensions X/Y: 110mm/220mm. Machine dimensions X/Y/Z: approx. 2200mm/950mm/1250mm, weight: approx. 1000kg. Documentation available. An on-site inspection is possible. Gcjdpfoxt Rmxox Aayea

Condition: used, Year of construction: 1982, grinding length:500 mm grinding width:225 mm workpiece height:400 mm total power requirement:5,5 kW weight of the machine ca.:3,4 t Gjdpocxxtmefx Aayoca NC81 NC-control, table belt drive 100-25000 mm/min., automatic feed, electronic dressing unit 020 NC-K with RPM-compensation, coolant pump, emergency cut-off

Condition: good (used), Work performed on the machine: New gel batteries (2 batteries) Hoses replaced Cleaning Specifications: Maximum operating time: 3 hours Maximum speed (km/h): 4 Voltage/frequency (V/Hz): 24 Protection rating: IPx4 Insulation class: III Rated power (W): 810 Airflow (l/sec.): 25.3 Vacuum (kPA): 11 Sound level at 1.50m (dB(A) ISO 3744): 65.8 Theoretical/actual coverage (m²/h): 2120/1275 Godpfoxflrmex Aayjca Working width (mm): 530 Maximum admissible slope (%): - Water flow rate (l/min): 0.5 to 1.1 Solution/recovery tank (l): 40/40 Squeegee width (mm): 760 Brush/pad diameter (mm): 530 Brush pressure (kg): 21 Brush rotation speed (rpm): 135 Number and type of brushes: 1 Disc Dimensions (L x W x H) (mm): 1190x510x1050 Weight in working order (kg): 221 Net weight (kg): 89

Condition: used, Year of construction: 2022, working length: 3,230 mm, pressing force: 130 t, Basic machine: TruBend 5130 (B23) Machine - C-frame construction - Press beam - Spherical bearing for press beam with press beam tilting - On-Demand Servo Drive with 4-cylinder technology - Y-axis position measuring system with dynamic deflection compensation - Hydraulic oil filling (lifetime filling) Backgauge - Gauge fingers (two units) Tool Clamping - TRUMPF hydraulic lower tool clamp Control - Touchpoint TruBend machine control - User management system Data Transmission - USB interface - RJ45 network interface - Network capability - Central Link - Remote support interface Operation - Operating unit with foot switches Gcjdpfxjxw U Iho Aayea - Communication rail - MobileControl Safety - CE marking and EC Machinery Directive compliance - Standard safety device - Lateral sliding doors - Rear roller gate Advanced Standard Configuration - Manual wedge crowning - 2-axis backgauge (X and R axes) - Manual TRUMPF upper tool clamp - Pneumatic lower tool displacement (I axis) - Integrated TRUMPF technology data - Operator panel: Support arm with height adjustment - Electrical cabinet air conditioning, rated for ambient temperatures up to 40°C Advanced machine equipment: - CNC-controlled wedge crowning - 4-axis backgauge (X, R, Z1, and Z2 axes) - TRUMPF hydraulic upper tool clamp - Bending technology data - Includes four standard materials (AlMg3, X5CrNi1810, St37, QStE380TM) - Uninterruptible power supply for the control (UPS) - Front work area illumination (LED) - Rear work area illumination (LED) - 2x support brackets with plastic support - BendGuard Technical Data: Machine - Press force: 1,300 kN - Bending length: 3,230 mm - Width between columns: 2,690 mm - Usable open height: 385 mm - Press beam tilt: ±10 mm - Throat depth: 420 mm - Table width: 120 mm Speeds - Rapid downward movement (with BendGuard option): 220 mm/s (approach), 25 mm/s (working) - X axis for 2/4/5-axis backgauge: 1,000 mm/s - R axis: 330 mm/s Traverse Paths, Stop Range - Y axis stroke: 215 mm - X axis traverse path: 600 mm - Maximum stop range in X direction: 860 mm - R axis traverse path: 250 mm Control, Hardware - User interface: Touchpoint TruBend - Basic hardware: Intel Core i5, 2.7 GHz, Dual Core processor; Windows Embedded Standard 7; 21.5" TFT color display with LED backlight; 1920 x 1080 pixel display resolution (Full HD) Operating Materials - Hydraulic oil volume: 115 l Connected Loads - Connected load (IEC), approx.: 17.5 kVA - Connected load (IEC), optional: 42 kVA - Compressed air connection: 6 bar ± 1 bar Dimensions and Weight - Length: 3,980 mm - Width: 1,900 mm - Height: 2,840 mm - Weight: 11,800 kg

Condition: excellent (used), Year of construction: 1999, functionality: fully functional, This machine is to carry out an alignment layer treatment of LCD glass substrate by a rotating roller. The roller and stage are flexible to change the setting of angle depending on the coditions used. Gcsdpfxjwli Eys Aayja

Year of construction: 2009, condition: ready for operation (used), Pressing force: 2300kN, bending length: 3230mm, ram stroke: 445mm, installation height: 615mm, distance between uprights: 2690mm, throat depth: 420mm, closing speed: 220mm/s, operating pressure: 300bar. Machine dimensions X/Y/Z: approx. 4300mm/2000mm/3200mm, weight: approx. 19200kg, operating hours: approx. 26830h. Documentation available. An on-site inspection is possible. Gsdpfx Aasxbhg Ejyeca

Year of construction: 2012, condition: ready for operation (used), Pressing force: 1700kN, bending length: 3230mm, ram stroke: 445mm, installation height: 615mm, distance between uprights: 2690mm, throat depth: 420mm, closing speed: 220mm/s, operating pressure: 300bar. Machine dimensions X/Y/Z: approx. 5250mm/2000mm/3000mm, weight: approx. 16000kg, operating hours: approx. 19133h. Documentation available. An on-site inspection is possible. Gedjxbhg Sopfx Aayeca

Year of construction: 2017, condition: used, machine/vehicle number: 21700430, Clamping force: 1,034 kN, heating plate dimensions: 700x500 mm, injection pressure: 1,500/2,000 bar, injection volume: 400 cm³, lightly used, the system must be professionally disconnected from the power supply. Gsdpfx Ajx Akh Ueayeca

Condition: used, Stack paper cutting machine, guillotine cutter, flatbed cutter SCHNEIDER Type Senator 155 Rubber, paper and veneer shear, plastic shear, fabric shear Rubber, paper and veneer shear Machine no. 60178 Year of manufacture 1968 Godpfodzqnyex Aaysca Cutting length: 1550 mm Cutting height: approx. 125 mm Feed height: 140 mm Back gauge: max. 1550 mm Knife drive motor power: 5.5 kW Power supply: 380 Volt, 50 Hz - Two-hand operation for blade stroke release - Automatic pressing by pressure clamp holds the paper stack on the table - Manual clamp and stroke release via foot pedal (operational) - Back gauge adjustment up to 1550 mm (can be adjusted manually via handwheel) - Retrofitted electrical control unit (not operational), no wiring diagrams, no user manual - Back gauge adjustment via servo motor (motor, controller, and control unit present, not operational) Required space (L x W x H): 325 x 270 x 165 cm Space required for transport without disassembly: length 330 cm x width 270 cm x height 175 cm Space required for transport with disassembly: length 550 cm x width 220 cm x height 175 cm (machine + separate table) Machine: length 270 cm x width 190 cm x height 175 cm Side table: length 240 cm x width 170 cm x height 120 cm Weight of assembled machine: approx. 5000 kg (excluding the transport steel plate) Good condition Ideal for cutting paper, cardboard, leather, cork, rubber, or fabric-reinforced rubber Sale price does not include the 20 mm steel plate the machine is stored on. (Price for the steel plate: 900 EUR net)

Condition: used, Year of construction: 2012, Year Modification / Upgrade 2012 Installation of Quadruplex Extrusion Line No. 02 for single tread production 2012 Foundation work for Quadruplex Extruder No. 02 2012 Installation of induction heating insert and die on Quadruplex Extruder No. 02 2013 Expansion of extrusion tooling for tread and sidewall production 2014 Two Siemens compact asynchronous motors 2017 New extruder screw (150 mm base size) for Quadruplex Extruder No. 2 2019 Closed-loop system upgrade (extended) 2021 Closed-loop system upgrade (extended) Gsdpfx Aajxb Uimoyjca 2022 New 200 mm screw for Troester extruders Control system: Modern control and visualization units (control desks, operator panels) Technical data: • Extruder screws up to 200 mm (2022) • Base screw 150 mm (2017) • Siemens asynchronous motors (2014) Maintenance / condition: Regularly modernized and upgraded from 2012–2022 Accessories / options: Conveyor systems, heating and cooling units, monitoring and measuring stations, winding equipment

Condition: used, functionality: fully functional, TASKI Swingo CO755 Automatic Cleaner and Scrubber-Dryer (internal article no. REI_001) Name: TASKI Swingo Drive: ELECTRIC Hand-held Condition: see photos / good condition Manufacturer: TASKI Model: Swingo CO755 Electric-operated 24 V 600 W 100-240 V 50-60 Hz 300 W Max. 155 kg Year of manufacture Integrated charger Fully charged battery Self-propelled forward and reverse Godpfx Aewlq Ebsayoca Charging current: 240 Scrub brush missing Price quoted upon pickup from warehouse 47441 Moers Various cleaners and scrubber-dryers in stock We offer as shown. Inspection is expressly offered. General: We offer various items here, which we describe as best as possible and provide informative photos. Further information about the item cannot be provided. We offer viewings on Tuesdays and Thursdays between 9 a.m. and 4 p.m. by appointment by phone. The item can be picked up immediately if required. Due to time constraints, we can only offer answers to this question if you provide us with a telephone number with your inquiry. Unless expressly stated, this item is USED. We offer it as shown. All items are ex warehouse, 47441 Moers. If you require shipping, please contact us to discuss packaging and shipping costs. (Shipping costs are approximately €150 net, depending on distance.) All dimensions are approximate.

Condition: good (used), Year of construction: 2020, operating hours: 22 h, Internal Article No.: 25019 Gcjdewq Nd Tspfx Aayoa Scrubber Dryer Nilfisk BA 751 Serial No.: 3510172302 101 Year: approx. 2020 / 2021 (not visible) Only approx. 21.5 operating hours! The machine works perfectly and will continue to be used until sold. Therefore, additional operating hours may be added.

Condition: used, Year of construction: 1962, Banbury Kneader / Mixer #3 with peripheral equipment Documented modifications / upgrades: Year Modification / Upgrade 1962 Gearbox upgrade Kneader III 1973 Carbon black weighing & dosing system for Kneader III 1981 Exhaust extraction system for Kneader III 1985 Batch-Off machine for Kneader 3 1985 Temperature control unit for Kneader 3 1995 DC motor 1500 HP, 1700 V, 1678 A 1996 Upgrade to KSBI-L270 Kneader III 2007 Hose scale for Kneader #3 2008 Vibration measurement system Mixer III 2008 Column-mounted slewing crane for bale handling Mixer III 2009 Vacuum hoist system Kneader III 2010 CMS system for Mixer III 2013 Long-strip cutting device for Kneader III 2014 Slab feeder for Kneader III Gsdpfxsxb T T Ro Aayoca 2014 Overnose conveyor Kneader III 2014 2 × floor scales for Kneader III 2014 New control system for Kneader III 2014 Cooling register MUAFAN 1+2 – cooling line mill Kneader 2+3 2015 Monitoring system (Kneaders I–III) for CMS Kneader III 2017 Mixer body replacement Kneader III 2023 Rubber kneader III KSBI-L270 Control system: New control system 2014, CMS system 2010, DC Drive / Automax, PLC Batch-Off & Conveyor, AC Drives documented Maintenance / condition: Regular modernizations and upgrades documented 1962–2023 Accessories / options: Batch-Off machine, slab feeder, put-up conveyor, long-strip cutter, floor scales, bale handling crane, vacuum hoist system, carbon black silos & weighing system, extruder, roller die, roller head with conveyor, cooling systems (dip tank, cooling line, laydown), control systems (DC Drive, AC Drive, Automax, PLC)

Condition: used, TASKI Swingo CO955 Automatic Cleaner and Scrubber-Dryer (internal article no. REI_002) Name: TASKI Swingo Hand-held Gjdpfx Aswlq I Aeayjca Condition: see photos / very good condition Manufacturer: TASKI Model: Swingo CO955 Electric-operated 24 V 1000 W 100-240 V 300 W Charging current: 240 V Max. 179 kg Year of manufacture Integrated charger Fully charged battery Self-propelled forward and reverse 2 disc brushes Price quoted upon pickup from the warehouse in 47441 Moers NEW PRICE: approx. €13,500 Various cleaners and scrubber-dryers in stock We offer as shown. Inspection is expressly offered. General: We offer various items here, which we describe as best as possible and provide informative photos. Further information about the item cannot be provided. We offer viewings on Tuesdays and Thursdays between 9 a.m. and 4 p.m. by appointment by phone. The item can be picked up immediately if required. Due to time constraints, we can only offer answers to this question if you provide us with a telephone number with your inquiry. Unless expressly stated, this item is USED. We offer it as shown. All items are ex warehouse, 47441 Moers. If you require shipping, please contact us to discuss packaging and shipping costs. (Shipping costs are approximately €150 net, depending on distance.) All dimensions are approximate.

Condition: used, Year of construction: 1999, Lot consists of: (1) X-Ray Machine Technical Details: Gcsdpfx Aaexfz Iwsyoa Upgraded Conveyor (2008), Climate Unit (2012)

Condition: used, operating hours: 172 h, overall weight: 1,500 kg, fuel type: electric, HAKO Automatic Cleaner and Scrubber-Dryer Name: HAKOMATIC B 1050 Drive: ELECTRIC Condition: see photos / TOP condition Item No.: B 1050 Manufacturer: HAKO Year of manufacture: see photos - visually TOP Operating hour meter reads "172" 4 brushes Electric-operated Battery, full power 36 V DC / 5.5 KW Weight: 1500 kg New price: approx. €39,900 Godowfflvspfx Aayoca Price quoted for pickup from the warehouse in 47441 Moers Various cleaners and scrubber-dryers in stock We offer them as shown. Inspection is expressly offered. General: We offer various items here, which we describe as best as possible and provide informative photos. No further information about the item can be provided. We offer viewings on Tuesdays and Thursdays between 9 a.m. and 4 p.m. by appointment. We offer viewings by telephone on Tuesdays and Thursdays between 9 a.m. and 4 p.m. The item can be picked up immediately if necessary. Due to time constraints, we can only offer answers to this question if you provide us with a telephone number with your inquiry. Unless expressly stated, this item is USED. We offer it as shown. All items are ex warehouse, 47441 Moers. If you require shipping, please contact us to discuss packaging and shipping costs. (Shipping costs are approximately €350 net, depending on distance.) All dimensions are approximate.

Condition: used, operating hours: 4,446 h, fuel type: electric, color: red, HAKO Automatic Cleaner and Scrubber-Dryer Name: HAKO B 750 R Drive: ELECTRIC Condition: see photos / good condition Used condition (please call for any defects) Battery is fully charged Wheels replaced - good tread Item No.: B 750 R Manufacturer: HAKO Year of manufacture: see photo - looks great Hour counter reads "4446" 2 brushes Electric-powered (Charger not included) New price: approx. €22,900 Gcsdpfx Aowffw Seayja Price quoted upon pickup from warehouse 47441 Moers Various cleaning and scrubber-dryers in stock We offer as shown. Inspection is expressly offered. General: We offer various items here, which we describe as best as possible and provide informative photos. Further information about the item cannot be provided. We offer the opportunity to view the item on Tuesdays and Thursdays between 9 a.m. and 4 p.m. by appointment by phone. The item can be picked up immediately if required. Due to time constraints, we can only offer answers to this question if you provide us with a telephone number with your inquiry. Unless expressly stated, this item is USED. We offer it as shown. All items are ex warehouse, 47441 Moers. If you require shipping, please contact us to discuss packaging and shipping costs. (Shipping costs are approximately €350 net, depending on distance.) All dimensions are approximate.